Express in Roman numerals:
\[i)105\]
\[ii)511\]

Hint: Here to express in Roman numeral break the number and decompose into sub groups and then wrap the terms to find the roman value.

Complete step-by-step solution:
To Express the numbers in Roman numerals, at the beginning let us understand the meaning of it.
Roman Numerals is a “number system” that uses a combination of letters to express a number. Hence, it is a numeral in a system of notation that is based on the ancient Roman system.
\[i)105\]
Let us find the roman numerical of \[105\]
Applying some rules to find the roman numerical
Split or break the given number (decompose it) into place value of subgroups i.e.,
\[105 = 100 + 5\]
Next, we need to convert each subgroup to Roman numerals i.e.,
\[100 = C\]
and
\[5 = V\]
In which in Roman numerals \[100\] is expressed as \[C\] and \[5\] is expressed as \[V\].
At final we need to combine up to the Roman Numerals, then substitute the Roman numerals for each sub groups i.e.,
\[105 = 100 + 5\]
\[105 = C + V\]
Therefore, \[105\] in Roman Numerals is expressed as:
\[105 = CV\]
Where, \[CV\] is a group of numerals in additive notation.
\[ii)511\]
In the same way let us find the roman numerical of \[511\]
Applying some rules to find the roman numerical
Split or break the given number (decompose it) into place value of subgroups i.e.,
\[511 = 500 + 10 + 1\]
Next, we need to convert each subgroup to Roman numerals i.e.,
\[500 = D\],
\[10 = X\] and
\[1 = I\]
In which, Roman numerals \[500\] is expressed as \[D\], \[10\] is expressed as \[X\] and \[1\] is expressed as \[I\].
Finally we need to combine up to the Roman Numerals.
Then substitute the Roman numerals for each sub groups i.e.,
\[511 = 500 + 10 + 1\]
\[511 = D + X + I\]
Therefore, \[511\] in Roman Numerals is expressed as:
\[511 = DXI\].
Where,
\[DXI\] is a group of numerals in additive notation.
Hence, in Roman Numerals the numbers are expressed as
\[i)105 = CV\]
\[ii)511 = DXI\]

Note: To express any number in Roman numeral follow the above rules to find the numeric value of the given number. Here are some of the notations which we follow while converting the values.
Additive notation is a group of two or more numerals, equal or sorted in descending order from high to low to calculate the value add up the symbols. Additive notation of the Roman numerals.